You can get an exponential growth if the time until the next technology decreases linearly with each technology.

For example the time until the next technology is 1/n, then the technologies per unit time increase exponentially.

This is true within a constant which is https://wikipedia.org/wiki/Euler%27s_constant

A justification for maybe why this is the right model is that the previous n technologies all help make the next technology possible in time ~1/n because they (n existing technologies) all contribute to innovating the next technology.